A compactness theorem in Finsler geometry

Abstract

Let (M.F) be a complete Finsler manifold and P be a minimal and compact submanifold of M. Rick(x), x in M is a differential invariant that interpolates between the flag curvature and the Ricci curvature. We prove that if on any geodesic c(t) emanating orthogonally from P we have ∫0∞Rick(t)>0, then M is compact.

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